Title: TWO PORT NETWORKS
1CHAPTER 6
2Chapter 62 PORT NETWORKS  DEFINATION
 WHAT IS PORT NETWORK
 It is a pair of terminals through which
 current may enter or leave a network.
 2 terminal devices or elements (resistors,
inductors or capacitors) results in one network  4 terminal or 2port circuit involves opamps,
transistor and transformer.  2port network is an electrical network with 2
separate ports for input and output as shown in
the figure a b 
3Chapter 6 2 PORTS NETWORKS DEFINATION
 2port network can be defined as voltagedriven
or current driven as shown below  V1 z11I1 z12I2
 V2 z21I1 z22I2
 In Matrix form
 V1 z11 z12 I2
I1  V2 z
 z21 z22 I1
I2
4Chapter 6 2PORTS NETWORK DEFINATION
 Z are called IMPEDANCE PARAMETERS OR Z PARAMETERS
 The z parameters are determined as below
 z11 V1 / I1 I2 0
 z12 V1 / I2 I1 0
 z21 V2 / I1 I2 0
 z22 V2 / I2 I1 0
5Chapter 62PORTS NETWORK DEFINATION
 The determination of zparameters are shown
below  z12 and z21 are called transfer impedance.
 If z11 z22 , the 2port network is symmetrical.
 If z12 z21 , the 2port network is reciprocal.


6Chapter 6 2PORT NETWORKS DEFINATION
 The Tequivalent circuit for reciprocal case (a)
and general equivalent circuit (b) is shown
below
7Chapter 6 2PORT NETWORKS zparameters
 EXAMPLE 1
 Determine the zparameters for the following
circuit 

8Chapter 6 2PORT NETWORKS zparameters
 SOLUTION FOR EXAMPLE 1
 1. Apply voltage source, V1 for the input
port and leave output port open as shown  2. Calculate z11
 z11 V1 / I1 (2040)I1/I1
 60
 3. Calculate z12
 z21 V2 / I1 40
 4. to calculate z12 z22, apply voltage
source to output port and leave input port open  z12 V1 / I2 40I2 / I2 40
 z22 V2 / I2 (3040)I2 / I2 70
 5. Thus, zparameters are
 z 60 40
 40 70
9Chapter 6 2PORT NEWTORKS zparameters
 EXERCISE 2 (Exercise Problem 19.1)
 1. Find the zparameter for the circuit shown
below 
10Chapter 6PORT NETWORKS zparameters
 Solution for EXERCISE 2
 1.Apply voltage source or current source at
input
11Chapter 6 2PORT NETWORKS
 EXERCISE 2 (CONTINUED)
 Apply voltage source at output and leave
input voltage open 
12Chapter 6 2port networks zparameters
13Chapter 6 2port networks zparameters
 EXERCISE 3
 Find the zparameters for the circuit below

14Chapter 6 2port networks zparameters
 EXERCISE 4
 Calculate I1 I2 for the 2port network
shown below 

15Chapter 6 2port networks Y parameters
 ADMITTANCE PARAMETERS
 Admittance is a reciprocal of the Impedance
 Y 1/Z
 In 2port network, it is defined as
 I1 y11 y12 V1 y V1
 I2 y21 y22 V2
V2
16Chapter 6 2port networks Y Parameters
 The value of yparameters are determined by

17Chapter 6 2port networks Y Parameters
 The yparameters are also called short circuit
admittance parameters  1. y11 shortcircuit input admittance
 2. y12 shortcircuit transfer admittance
 (port 2 to 1)
 3. y21 shortcircuit transfer admittance
 (port 1 to 2)
 4. y22 shortcircuit output admittance
 The unit for Admittance is S (Siemens)
18Chapter 6 2port networks Y Parameters
 A reciprocal network (when y12 y21) and a
equivalent circuit general equivalent cct. 
19Chapter 6 2port networks Y Parameters
 EXAMPLE 2
 Determine the yparameters for network
shown below 
20Chapter 6 2port networks Y Parameters
 SOLUTION FOR EXAMPLE 2
 1. Shortcircuit output port (V2 0V)
 V1 I1 (4//2) 4/3 I1
 y11 I1 / V1 I1 / 4/3 I1 0.75
s  I2 (4/(42))I1 2/3 I1 (Use
current Division )  y21 I2 / V1 0.5s
 2. To get other yparameters, shortcircuit
input port (V1 0V)  and connect current source, I2 to output
port.  V2 I2 (8//2) 8/5 I2
 y22 I2 / V2 I2 / 8/5 I2 0.625 s
 I1 (8/(82))I2 4/5 I2 (Use
current Division )  y12 I1 / V2 0.5s
 3. The yparameters are
 y 0.75 0.5
 0.5 0.625
21Chapter 6 2port networks Y Parameters
 EXERCISE 5
 Determine the yparameters for the T Network
shown below 
22Chapter 6 2port networks Defination Hybrid
Parameters
 Z and y parameters in the 2port network do not
always exits. Thus , need to create another set
of parameters which are called Hybrid parameters
and defined as below  V1 h11 h12 I1 h I1
 I1 h21 h22 V2
V2
23Chapter 6 2port networks Defination Hybrid
Parameters
 The hparameters are also called hybrid
parameters defined as below  1. h11 shortcircuit input impedance
 2. h12 opencircuit reversed voltage gain
 3. h21 shortcircuit forward current gain
 4. h22 opencircuit output impedance
24Chapter 6 2port networks Hybrid Parameters
 For the reciprocal network,
 h12 h21
 Hybrid model for 2port network

25Chapter 6 2port networks Inverse Hybrid or g
Parameters
 The inverse or reciprocal of Hybrid parameter
will produce gparameter and defined as below  g11 I1/V1 I2 0
 g12 I1/I2 v1 0
 g21 V2/V1 I2 0
 g22 V2/I2 v1 0
 I1 g11 g12 V1 g
V1  V2 g21 g22 I2
V2
26Chapter 6 2port networks Inverse Hybrid or g
Parameters
 The model of gparameters are shown below
 The hparameters are also called inverse hybrid
parameters defined as below  1. g11 Opencircuit input impedance
 2. g12 Shortcircuit reversed current gain
 3. g21 Opencircuit forward voltage gain
 4. g22 Shortcircuit output impedance
27Chapter 6 2port networks Defination Inverse
Hybrid or g Parameters
 EXAMPLE 3
 Determine the hparameters for network
shown below 
28Chapter 6 2port networks Defination Inverse
Hybrid or g Parameters
 SOLUTION FOR EXAMPLE 3
 1. Find h11 h21 by shortcircuit the
output port and connect input port to current
source, I1  V1 I1 (23 // 6) 4I1
 h11 V1 / I1 4
 next, use current division to obtain h21
 h21 I2 / I1 6/(63)I1
2/3  2. Find h22 h12 by opencircuit the input
port and connect output port to voltage source,
V2
29Chapter 6 2port networks Inverse Hybrid or g
Parameters
 V1 V2 6 /(63) 2/3 V2
 h12 V1 / V2 2/3
 next, use voltage division to find h22
 h22 I2 / V2 I2 /(63)I2
2/3  3. The hparameters are
 h 4 2/3
 2/3 1/9
30Chapter 6 2port networks Inverse Hybrid or g
Parameters
 The equivalent cct to compute hparameters are
shown below 
31Chapter 6 2port networks Inverse Hybrid or g
Parameters
 EXERCISE 6
 Determine the hparameters for the T Network
shown below 
32Chapter 6 2port networks Inverse Hybrid or g
Parameters
 EXERCISE 7
 Determine the hparameters for the Network
shown below 

33Chapter 6 2port networks Inverse Hybrid or g
Parameters
 The gparameters can be expressed in term of
function of s (Laplace domain)  For IH Inductor sL s
 For 1F Capacitor 1/sC 1/s
 To obtain g11 and g21 SC Output port Connect
voltage source to Output port  To obtain g22 and g12 SC Input port Connect
current source to Output port
34Chapter 6 2port networks Inverse Hybrid or g
Parameters
 EXAMPLE 4
 Determine the gparameters in sdomain for
Tnetwork shown below 
35Chapter 6 2port networks Inverse Hybrid or g
Parameters
 Solution for Example 4
 1. Determine g11 g21
 Use Voltage Division to calculate I1
 V2
 I1 1 / (s 1) V1
 g11 I1 / V1 1/(s1)
 V2 1 / (s 1) V1
 g21 V2 / V1 1/(s1)
36Chapter 6 2port networks Inverse Hybrid or g
Parameters
 Solution for Example 4 (Continued)
 2. Determine g22 g12
 Use Voltage Division to calculate I1
 V2
 I1 1 / (s 1) I2
 g12 I1 / I2 1/(s1)
 V2 (1/s) (s//1) I2
 g22 V2 / I2 (s2 s 1)/ s(s1)
37Chapter 6 2port networks Inverse Hybrid or g
Parameters
 The equivalent cct to
 determine gparameters
 in the sdomain
38Chapter 6 2port networks ABCD parameters
 ABCD is also called Transmission Parameters where
the current I1 is entering the network while the
current I2 is leaving the network.  The input parameters are described in term of
output parameters  V1 A B V2 T V2
 I1 C D I2
I2  The ABCD parameters are used in the design of
telephone systems, microwave networks radars.
39Chapter 6 2port networks ABCD parameters
 The ABCD parameters are defined as below
 A V1 / V2 I2 0 B V1 / I2
V2 0  C I1 / V2 I2 0 D I1 / I2
V2 0  The transmission parameters are called as
 1. A Opencircuit voltage ratio (unit
less)  2. B Negative shortcircuit transfer
impedance ()  3. C Opencircuit transfer admittance
(Siemens)  4. D Negative shortcircuit current ratio
(unit less)  It provides a direct relationship between input
and output variables and very useful in cascaded
network.  Network is reciprocal if AD BC 1

40Chapter 6 2port networks abcd parameters
(inverse transmission
parameters)
 For Inverse Transmission Parameters, Output
parameters are described in term of Input
parameters.  V2 a b V1 t V1
 I2 c d I1
I1  The Inverse transmission parameters are
reciprocal if AD BC 1, ad bc 1  It is determined as below
 a V2 / V1 I1 0 b V2 / I1
V10  c I2 / V1 I1 0 d I2 / I1
V10
41Chapter 6 2port networks ABCD parameters
 EXAMPLE 5
 Find the ABCD parameters for the circuit shown
below 


42Chapter 6 2port networks ABCD parameters
 Solution for Example 5(Continued)
 1. Connect Voltage source, V1 to the
 input port and let output port open.
 2. Perform nodal analysis at node 1 2


43Chapter 6 2port networks ABCD parameters
 Solution for Example 5(Continued)
 3. Determine C,
 4. Determine A
 5. Determine B D by connecting input source
to the input  port and output port is shortcircuit.

44Chapter 6 2port networks ABCD parameters
 Solution for Example 5(Continued)
 6. Redraw the cct as below
 7. Once again, perform nodal analysis


45Chapter 6 2port networks ABCD parameters
 EXERCISE 8 (Practice Problem 19.36)
 Find I1 I2 if the transmission parameters
for the 2 port networks in circuit below are  5 10
 0.4s 1
46Chapter 6 2port networks Interconnection
 The six parameters for 2port networks are
 1. zparameters
 2. yparameters
 3. hparameters
 4. gparameters
 5. ABCDparameters
 6. abcdparameters
 All this parameters are interrelated.
 The relationship between yparameters and
zparameters are shown below  y11 z22 / z 2. y12 z12 / z 3. y21
z21 / z  4. y22 z11 / z where z is determinant of z
47Chapter 6 2port networks Interconnection
 The relationship between hparameters
zparameters are shown below  1. h11 z / z22 2. h12 z12 / z22
 3. h21 z21 / z22 4. h22 1 / z22
 where z is determinant of z
 The Conversion of 2port parameters are shown in
table 19.1
48Chapter 6 2port networks Interconnection
 EXAMPLE 6 (Practice problem 19.10)
 Determine y T of 2port network where
zparameters are defined below  z 6 4
 4 6
49Chapter 6 2port networks Interconnection
 Solution for Example 6
 1. Calculate determinant of z
 z (6)(6) (4)(4) 20
 2. Use table 19.1, y 0.3 0.2

0.2 0.3  y11 z22 / z 6/20 0.3
 y12 z12 / z 4/20 0.2
 y21 z21 / z 4/20 0.2
 y22 z11 / z 6/20 0.3
 3. A z11 / z21 6/4 1.5
 B z / z21 20/4 5
 C 1/z21 1/4 0.25
 D z22 / z21 6/4 1.5
50Chapter 6 2port networks Interconnection
 The six parameters are used for the
interconnection of 2port networks for the
following connection  1. Series Connection Use Impedance

Parameters  2. Parallel Connection Use Admittance

Parameters  3. Cascaded Connection Use Transmission

Parameters  4. Series Parallel Connection Use Hybrid

Parameters  5. ParallelSeries Connection Inverse
Hybrid
51Chapter 6 2port networks Interconnection
 Series Connection
 Zparameter for series network
 z z11a z11b z12a z12b
 z21a z21b z22a
z22b 

52Chapter 6 2port networks Interconnection
53Chapter 6 2port networks Interconnection
 Cascade Connection
 A B Aa Ba Ab Bb
 C D Ca Da Cb Db

 T Ta Tb
54Chapter 6 2port networks Interconnection
 SeriesParallel Connection
 h ha hb
 ParallelSeries Connection

 g ga gb
55Chapter 6 2port networks Interconnection
 EXAMPLE 7 (Exercise problem 19.67)
 Find the transmission parameters, T.
56Chapter 6 2port networks Interconnection
 SOLUTION FOR EXAMPLE 7
 1. Obtain yparameters then converted to z
 and then converted to T by using
 Conversion table.
 2. The yparameter for upper network are
 3. Determine the determinant of y
 parameter
 (2)(2) (1)(1) 3
 4. Convert to zparameters, Za Zb
 Za y22 / y y12 / y
2/3 1/3  y21 / y y12 / y
1/3 2/3 
57Chapter 6 2port networks Interconnection
 SOLUTION FOR EXAMPLE 7
 5. zb 1 1
 1 1
 6. z za zb 5/3 4/3
 4/3
5/3  7. now, calculate determinant of z, z
25/9 16/9 1  8. From, the conversion table, determine
transmission parameter, T  T z11/z21 z / z21
1.25 0.75  1/z21 z22 / z21
0.75 1.25
58Chapter 6 2port networks Interconnection
 EXERCISE 9 (Exercise Problem 19.70)
 For the parallelseries connection of 2port
network, find gparameters. 
